The proposed research is concerned with the theory of Azumaya algebras over a commutative ring. The principal investigator will examine the possibility of a presentation of the 2-torsion Brauer group of certain commutative rings. Working with the coordinate rings of surfaces, the project will try to measure the failure of this presentation in terms of the geometry of the surface. This research is in the general area of algebra and is an interesting combination of algebra, number theory and algebraic geometry. Given a surface it is possible to associate with it a coordinate ring and with this ring a group. This project will examine properties of this group in an effort to determine the geometry of the surface.
